Vorskla offered little in reply as their hopes of reaching the last 32 ended with a whimper, with Arsenal expending minimal energy en route to the victory ahead of Sunday's North London derby against Tottenham Hotspur.
The match kicked off in front of thousands of empty seats following the late change of venue from Poltava to Kiev's NSC Olimpiyskiy, where both the atmosphere and the temperature were significantly colder than when the stadium hosted the Champions League final in May.
Arsenal eventually warmed to conditions which dropped as low as -12°C, but it was Vorskla who started the brighter and could have taken the lead as early as the third minute when Yury Kolomoets blasted over after Arsenal were slow to react to a quick free kick.
Vladimir Chesnakov had a couple of sights of goal in quick succession moments later - the best of which drew a routine save from Petr Cech - but that is about as good as it got for the hosts in the first half as Arsenal soon took complete control of the contest.
Ainsley Maitland-Niles drew the first save from Bogdan Shust soon before the opening goal, which was fired into an empty net by Smith Rowe after Eddie Nketiah's barraging run into the box forced Artur to poke the ball away from the hands of his own goalkeeper.
Ramsey pulled rank to fire one free kick off target before he doubled Arsenal's advantage, winning and dispatching a penalty having been brought down by Igor Perduta inside the area.
It was fast turning into a miserable night for the hosts - already forced to play more than 200 miles away from their own stadium - and Arsenal looked to be in no mood to let up as Willock and Nketiah both came close in quick succession.
Vorskla were not helping themselves with some dreadful defending, though, and they conceded a third shortly before half time when Willock was allowed to carry the ball to the edge of the box, open his body and curl his finish into the bottom corner for his first ever Arsenal goal.
With the victory - and with it top spot in the group - effectively wrapped up by half time, Unai Emery used the second 45 minutes to hand debuts to Zech Medley, Bukayo Saka and Charlie Gilmour as Arsenal ended the match with six teenagers on the field.
There were chances to add to their advantage, with Willock seeing one tame effort saved and Smith Rowe having a goal belated chalked off - seemingly for offside - after firing Stephan Lichtsteiner's cross into the roof of the net.
A closer match might have spawned more vociferous appeals against the debatable decision, but Vorskla never looked like getting back into the game even when Perduta squandered their best chance after the ball had fallen kindly to him inside the area.
Arsenal went straight up the other end and forced another save from Shust through Smith Rowe, while the Vorskla keeper was also called into action to deny Saka and Willock in the closing stages.
Nketiah put another chance wide of the target before the home side wasted one last opening to rescue some consolation from a thankless evening when Nicolas Careca curled an effort off target in the third minute of stoppage time.
Vorskla could have no complaints at the final score, though, as they were comfortably second best en route to a fourth successive defeat across all competitions and their third home defeat of the group stages.
Arsenal, meanwhile have now kept three consecutive away clean sheets in Europe for the first time since their run to the 2005-06 Champions League final and are unbeaten in 18 games across all competitions ahead of a testing week which sees them take on Spurs and Manchester United in their next two league games.
VORSKLA STARTING XI: Shust; Perduta, Dallku, Chesnakov, Artur; Sapai (Careca 36'), Sklyar, Sharpar, Rebenok (Sakiv'); Kulach (Kane 71'); Kolomoets
ARSENAL STARTING XI: Cech; Lichtsteiner, Jenkinson, Holding (Medley 60'), Maitland-Niles; Guendouzi (Gilmour 76'), Elneny; Willock, Ramsey (Saka 68'), Smith Rowe; Nketiah